A normally distributed data has been

Question

A normally distributed set of data has been generated where 50% of the data lies below 97 and 70% lies below 104. Determine the mean and standard deviation of this data.

Answer 1

It's given that mean (μ)  = 97.  You want to find sigma, the std. deviation (σ).

 

Using the formula for Z score, Z₁₀₄ = (104 - 97) / σ.

 

I asked my TI-83 calculator what is the Z score for 70%, using command (in DISTR menu)

 

invnorm(0.70) and the answer is 0.5244.

 

Thus I have the equation 7 / σ = 0.5244, from which we have

σ = 7 / 0.5244 = 13.55

Answer 2

Can you figure out what information about the mean is given in the mean is given in the question?